1 answer:
Answer:
C.
Step-by-step explanation:
Find the rate of change/slope (m) using two pairs (1, 8) and (2, 12):
(Note: M(x) = y)
Find y-intercept (b) by substituting x = 1, M(x) = 8, and m = 4 in M(x) = mx + b.
Thus:
8 = (4)(1) + b
8 = 4 + b
Subtract 4 from each side
8 - 4 = b
4 = b
b = 4
substitute m = 4, and b = 4 in M(x) = mx + b, to get the equation that models the relationship.
The equation would be:
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Answer:
They are similar by the definition of similarity in terms of a dilation
Step-by-step explanation:
The given vertices of triangle ΔABC are;
A(1, 5), B(3, 9), and C(5, 3)
The vertices of triangle ΔDEF are;
D(-3, 3), E(-2, 5), and F(-1, 2)
Therefore, we get;
The length of segment, = √((9 - 5)² + (3 - 1)²) = 2·√5
The length of segment, = √((9 - 3)² + (3 - 5)²) = 2·√10
The length of segment, = √((5 - 3)² + (1 - 5)²) = 2·√5
The length of segment, = √((5 - 3)² + (-2 - (-3))²) = √5
The length of segment, = √((2 - 5)² + (-1 - (-2))²) = √10
The length of segment, = √((2 - 3)² + (-1 - (-3))²) = √5
∴ /
= 2·√5/(√5) = 2
/
= 2·√10/(√10) = 2
/
= 2·√5/(√5) = 2
The ratio of their corresponding sides are equal and therefore;
ΔABC and ΔDEF are similar by the definition of similarity in terms of dilation.